Find an unknown element in a matrix given only a triangular matrix, elements of major diagonal and the determinant

Question

Given that matrix P is a triangular matrix and the elements of its major diagonal is given as

$p(11) = 2$,

$p(22) = -3$

$p(33) = 3b$ , find the value of b if $|P| = -36$

I tried finding the inverse then the adjoint but it didn't work out, this question has only 2 marks, any help would be appreciated

Answer 1

Hint: The determinant of a triangular matrix is the product of its diagonal